Regularized low-coherence overcomplete dictionary learning for sparse signal decomposition

Abstract

This paper deals with learning an overcomplete set of atoms that have low mutual coherence. To this aim, we propose a new dictionary learning (DL) problem that enables a control on the amounts of the decomposition error and the mutual coherence of the atoms of the dictionary. Unlike existing methods, our new problem directly incorporates the mutual coherence term into the usual DL problem as a regularizer. We also propose an efficient algorithm to solve the new problem. Our new algorithm uses block coordinate descent, and updates the dictionary atom-by-atom, leading to closed-form solutions. We demonstrate the superiority of our new method over existing approaches in learning low-coherence overcomplete dictionaries for natural image patches.